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Simplifying abs(2x + 8) = abs(x + 4) Reorder the terms: abs(8 + 2x) = abs(x + 4) (8 * abs + 2x * abs) = abs(x + 4) (8abs + 2absx) = abs(x + 4) Reorder the terms: 8abs + 2absx = abs(4 + x) 8abs + 2absx = (4 * abs + x * abs) 8abs + 2absx = (4abs + absx) Solving 8abs + 2absx = 4abs + absx Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4abs' to each side of the equation. 8abs + -4abs + 2absx = 4abs + -4abs + absx Combine like terms: 8abs + -4abs = 4abs 4abs + 2absx = 4abs + -4abs + absx Combine like terms: 4abs + -4abs = 0 4abs + 2absx = 0 + absx 4abs + 2absx = absx Add '-1absx' to each side of the equation. 4abs + 2absx + -1absx = absx + -1absx Combine like terms: 2absx + -1absx = 1absx 4abs + 1absx = absx + -1absx Combine like terms: absx + -1absx = 0 4abs + 1absx = 0 Factor out the Greatest Common Factor (GCF), 'abs'. abs(4 + x) = 0Subproblem 1
Set the factor 'abs' equal to zero and attempt to solve: Simplifying abs = 0 Solving abs = 0 Move all terms containing a to the left, all other terms to the right. Simplifying abs = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Add '-1x' to each side of the equation. x + -1x = -4 + -1x Combine like terms: x + -1x = 0 0 = -4 + -1x Simplifying 0 = -4 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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